Independent-measures t-test

Description

The t-test gives an indication of
the separateness of two sets of measurements, and is thus used to check whether
two sets of measures are essentially different (and usually that an experimental
effect has been demonstrated).

The independent-measures t-test (or independent t-test) is used when
measures from the two samples being compared do not come in matched pairs.

It is used when groups are independent and all people take only one test
(typically a post-test). In design
notation, this is:

R

X

O

R

O

The requirement for Variance homogeneity
test may be measured with Levene's test. Results for this can be given in
SPSS along with the t-test results.

Calculation

The value of t may be calculated using packages such as SPSS. The actual
calculation for two groups is:

t = experimental effect / variability

= difference between group means /standard
error of difference between group means

= Dg / SEg

Dg = AVERAGE(Xt) - AVERAGE(Xc)

where Xt are the measures in the
treatment group and Xc are the measures in the control group. Note
that any minus sign is removed, so that 't' remains positive.

SEg = SQRT( VAR(Xt)/nt
+ VAR(Xc)/nc)

where n is the number of people in the group and
VAR(X) is the variance of X.

VAR(X) = SUM((X-AVERAGE(X))2)/(n-1)

A single group can also be compared with a measure, M, taken
elsewhere.

t = (AVERAGE(X) - M) / (STDEV(X) / SQRT(n) )

Where STDEV(X) is the standard deviation of the
group.

Interpretation

The resultant t-value is then looked up in a
t-test table
to determine the probability that a significant difference between the two sets
of measures exists and hence what can be claimed about the efficacy of the
experimental treatment.

Effect

The t-value can also be converted to an r-value to measure
effect, which can be calculated as: